How?
They 'pump the market' because buying bitcoin increases its scarcity, thus raising the price.
You're asking what the utility of stablecoins is: Stablecoins are widely used as a legislatively advantageous on- and off-ramp for the whole crypto market.
Off-ramp: If people want to sell BTC or other volatile tokens because they want to realize profits, the obvious thing would be to sell for fiat (USD/EUR). But due to taxation and legislation this is often difficult. Stablecoins like Tether provide the utility of a low-volatility currency that fiat would fill. Main advantage is bypassing legislation.
This use is so common there is jargon for "Tethering up".
There also exist many debit cards that allow paying with stablecoins, increasing utility. The rise of DeFi and money markets for stablecoins also provides a good return on stablecoins while in theory being low-volatility.
On-ramp: If people want to buy a certain token they first go into Tether. This is usually for bypassing local legislation limiting the buying of a specific token or use of exchanges. This use is less common, I would wager.
Of course, for any of this to be actually useful Tether has to remain the same price. If Tether starts to deviate significantly from the 1USD peg, a liquidity crisis cuold be triggered.
Personally, I haven't trusted Tether since the first BitFinex scandals and avoid it like the plague. For my stablecoin needs, I use something that is audited and over-collateralized like DAIv2.
That alone should be a red flag.
I know there are a lot of narratives about people in repressive governments using Bitcoin to take their meager savings out of the country or carrying their net worth across borders in mind wallets, but Tether isn't targeting these people.
Tether has very high minimum purchases. They cater (supposedly) to extremely wealthy clients who, for whatever reason, would rather use a questionable intermediary instead of going straight to any one of the major financial institutions offering BTC to purchase their bitcoin. If you had told me in 2015 that it was difficult to purchase BTC as an institution, I would have believed you. In 2021, there isn't much reason to do end-runs around regulations unless you're deliberately trying to launder money and/or dodge taxes.
Bitfinex doesn't exactly have a reputation that deserves any trust, so I wouldn't put it past them.
I think there is a good reason Coinbase does not allow trading Tether.
